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Modeling Player Performance in Rhythm Games

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Modeling Player Performance in Rhythm Games Modeling Player Performance In Rhythm Games Lingfeng Yang⇤ Square-Enix Research Center CR Categories: I.2.1 [Artificial Intelligence]: Applications and Player modeling. Recently, game companies have shown inter- Expert Systems—Games H.5.5 [Information Interfaces and Presen- est in crafting games that adapt to individual players, driving aca- tation]: Sound and Music Computing—Modeling I.3.6 [Computer demic research efforts in player modeling. Some work in this area Graphics]: Methodology and Techniques—Interaction techniques focuses on modeling player satisfaction in platform games [Peder- sen et al. 2009]. Other work is concerned with modeling player Keywords: interaction, games, music cognition, probabilistic in- performance and using it to predict player behavior [Drachen et al. ference 2009]. Here, we are interested in modeling player performance in rhythm games and how the models can be used to facilitate skill development. Algorithmic music and composition. A primary research prob- lem in algorithmic music is the generation of complete musical pieces in a given style. This often involves building statistical mod- els of music. A survey of modeling and generation techniques can be found in [Conklin 2003]. Here, we are interested in how statisti- (a) Reference song cal music models can be adapted for modeling music performance in the rhythm game setting. As a starting point, we adapt a Markov model. In future work, we hope to apply this approach with more complex models to realistic settings. 2 Modeling Rhythm Game Performance 2.1 Background (b) User input In a rhythm game, the player hits notes by pressing buttons on an input device. The goal is to hit notes in time to the music, which can be represented as a sequence S of note, time pairs: N S := si =(ni,ti),ni C, ti R,t1 <t2 <...tN i=1, { 2 2 } where C is a finite set of possible notes, and N the total number of notes in the song. Chords, or sets of in-game notes that occur at the (c) Missed notes (shaded) same ti, are represented as a distinct note. During the game, notes ni in S appear on screen in chronologi- AB C AB C cal order. The player then receives visual and aural cues to hit each A 0.17 0.33 0.5 A 0 0.5 0.33 ni at time ti. The player is allowed to press the buttons correspond- B 0.5 0.125 0.375 B 0.5 0 0.33 ing to the notes in any way he wishes. After all the notes from S C 0.11 0.55 0.33 C 0.0 0.2 0.33 have appeared, the player will have produced a sequence of button (d) (Left) Learned order-1 Markov transition table for presses P (ni ni 1). (Right) Our corresponding skill model: miss rates | − P (mi ni,ni 1). Table layout: (row, column) (ni 1,ni). | − ! − M I := (ni,ti),ni N,ti R i=1 { 2 2 } Figure 1: The method at a glance: We represent songs with time- where M is the number of notes actually hit. lines, where A, B, C are the set of possible notes, and the bars We consider a measure of skill to be a measure of how closely represent specific occurences them in the song. (a) is a reference S and I match. Moreover, we are also concerned with informative song and (b) is a performance of the song by the player. We com- critera; those that the player can improve intuitively and directly. bine (a) and (b) to obtain a labeling of missed notes (c) and learn Although there are many ways to describe the differences between a conditional probability distribution (d) describing the probability S and I, the one we focus on is the missed note; where there is no of missing a note given immediately previous notes. ij I that matches a particular sk S in the time component (within2 a reasonable timing window). 2 For each si S, we compare with all i I and label it as 2 2 1 Introduction, Related Work missed if there is no close enough i. This definition is useful be- cause it covers many different kinds of mistakes, from playing the We present a method for modeling skill level in a rhythm game wrong note, to getting the rhythm of the song incorrect, but is still by building probabilistic models of how well the player is able to informative. A limitation of this labeling is that it does not capture match a technically perfect execution. This enables applications for the class of mistakes where the player plays too many notes. Nev- facilitating skill improvement in rhythm games. ertheless, we will see that tracking missed notes still gives useful information about the skill of a player and where it needs improve- ⇤e-mail: [email protected] ment. Copyright is held by the author / owner(s). SIGGRAPH Asia 2010, Seoul, South Korea, December 15 – 18, 2010. ISBN 978-1-4503-0439-9/10/0012 2.2 Determining miss rate from a Markov model. technique are identified by the musician or his instructor, and tech- We first learn an order-k (we currently use k =1) Markov chain nical exercises are prescribed to address them. that records the conditional probability of each note occuring in the It is often not clear to the rhythm game player which exercises reference song given the previous notes. The states of our Markov should be played in order to improve the fastest. Moreover, it is also often the case that no existing exercise addresses the unique model are the notes ni C; i.e., in this model, ni (in si =(ni,ti)) 2 technical shortcoming of the player; one then has to put in manual is conditionally independent of all others given ni 1. As the player plays through S, he generates input− I and missed work to devise individualized exercises. With our skill model, it is possible to automate the generation of such exercises. One way notes of S are labeled. Let mi be an indicator random variable is to simply generate repetitions of the most-often-missed note se- tracking whether si is missed. We consider mi to be conditionally quences. More sophsticated exercise generation algorithms would dependent on ni,ni 1. This gives rise to the conditional distribu- − draw on techniques from algorithmic music. tion of missed notes P (ni mi,ni 1) along with the overall condi- | − tional probability of missing P (mi ni 1). Then the miss rate of ni | − 4 Prototype Game in the note sequence ni,ni 1 is obtained using Bayes’ rule and the aforementioned probabilities:− As a platform for testing these ideas, we developed a rhythm game whose mechanics are based on that of the popular DJ simulator Beatmania IIDX. We chose Beatmania IIDX because it already has P (ni mi,ni 1) an established repretoire of songs, simple button-based controls, P (mi ni,ni 1)= | − P (mi ni 1) | − P (ni ni 1) | − and an active mod/content creation community. In our prototype, | − the model’s parameters are trained simply by having the user play Learning the miss rate. We employ a frequency-based estimator the game normally. The advantage of this is that the training pro- to learn the conditional probabilities given a song-input pair S, I. cess requires no additional interaction beyond what the user already If the order of the Markov model k is sufficiently small, useful expects to do playing a rhythm game. After each song is played, conditional probabilities can be learned in the context of a single the game records the statistics for that song and appends it to a playthrough of a single song. See Figure 1 for an example of how database. An exercise is generated from the statistics after each the model is learned from user input given a small but sufficiently song is played, and the player has the option of using it for practice. covering sequence of notes. 5 Discussion, Future Work Variable-order models. As the player’s proficiency increases, it becomes harder to capture technical shortcomings in a meaningful An in-depth user study needs to be conducted to quantify the degree way using a Markov model with fixed order k. This is because the to which the exercise generation and difficulty prediction features errors made depend on an increasingly longer history of notes. If are effective in improving skill and accuracy, and to compare dif- there is a particular note sequence of length n>kthat the player ferent methods of generating the exercise material in order to select consistently makes mistakes on, but the model is order k, and the the best method. player does not usually make mistakes on the last k notes of that One avenue for future work is to augment this approach with sequence, the miss rate for that problematic sequence will be ar- more complex models drawn from algorithmic music generation, tifically low. Conversely, calculating miss rates using order k for such as stochastic L-system grammars, which can capture longer- sequences where m<kwould do suffers from the sparse data ranged aspects of compositions (and potentially, technique). An- problem. This suggests augmenting our technique with variable- other is to take the idea of skill modeling in general and apply it to order Markov models (also used extensively in music modeling), other types of games. which allow for each state to be dependent on a varying number of An interesting long-term direction is to use this approach to as- previous states instead of a fixed k states, and for which learning sist training in actual musical instruments.
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